Changes in the sources of growth of labour productivity can be examined more systematically using the concept of growth accounting which has been widely employed by economic historians to benchmark performance (Crafts, 2009). The basic approach assumes that GDP is accounted for by the employment of factor inputs and their productivity Total Factor Productivity (TFP) as follows:
Y = AKαLβNγ
where Y is output, K is capital, L is labour, N is land and A is TFP while α, β and γ are the
elasticities of output with respect to capital, labour and land, respectively. The level of TFP reflects the state of technology and it is usually measured as a residual after the other items in the expression have been measured. This can be converted into an equation to account for the proximate sources of output growth
ΔY/Y = αΔK/K + βΔL/L + γΔN/N + ΔA/A
and a growth accounting equation for labour productivity growth Δln(Y/L) = αΔln(K/L) + γΔln(N/L) + ΔlnA
The latter gives a decomposition of the percentage rate of growth of labour productivity into a contribution from the percentage rate of growth of capital per labour input (capital deepening), of land per labour input (land deepening) and a term based on the percentage growth rate of TFP. In implementing this approach in Table 2.5, it is assumed that factor shares are a reasonable approximation for the output elasticities.
Table 2.5 Growth accounting estimates (% per year) (a) Output growth
Capital inputs contribution
Labour inputs contribution
Land inputs contribution
TFP growth
Real GDP growth 1760–1800 0.35*1.0 = 0.35 0.50*0.8 = 0.40 0.15*0.5 = 0.08 0.4 1.2 1800–1830 0.35*1.7 = 0.60 0.50*1.4 = 0.70 0.15*0.1 = 0.02 0.4 1.7 1830–1860 0.35*2.5 = 0.88 0.50*1.4 = 0.70 0.15*0.1 = 0.02 0.7 2.3 (b) Labour productivity growth
K/L growth N/L growth TFP growth Y/L growth 1760–1800 0.35*0.2 = 0.07 0.15*–0.3 =
–0.04
0.4 0.4
1800–1830 0.35*0.3 = 0.10 0.15*–1.3 = –0.20
0.4 0.3
1830–1860 0.35*1.1 = 0.38 0.15*–1.3 = –0.20
0.7 0.9
Note: All estimates are derived on standard neoclassical assumptions with the weights as follows:
capital = 0.35, land = 0.15, labour = 0.5.
Sources: Crafts (1985), (2005) revised with land growth from Allen (2009b) and real GDP growth based on Broadberry et al. (2015).
Table 2.5 reports that the rate of TFP growth nearly doubled from 0.4 per cent per year in 1760–1800 to 0.7 per cent per year in 1830–1860. This certainly can be interpreted as reflecting acceleration in the rate of technological progress but TFP growth captures more than this. No explicit allowance has been made for human capital in the growth accounting equation. Prior to 1830, it is generally agreed that any contribution from extra schooling or improved literacy was negligible, but in the period 1830–60 education may have accounted for around 0.3 percentage points per year of the measured TFP growth in Table 2.5 (Mitch, 1999). From 1760 to 1800, there is good reason to think that average hours worked per worker per year were increasing which is not taken into account in Table 2.5; the increase was probably enough to imply a correction to labour inputs growth sufficient to push TFP growth from technological progress down quite close to zero (Voth, 2001). More generally, it seems very likely that much of the increase in real GDP per person from the mid-fifteenth to the late eighteenth centuries came from people working longer rather than from technological advance (Broadberry et al., 2015, pp. 260–265). Overall then, a best guess might be that the contribution of technological progress, as reflected in TFP growth, went from about zero to a sustained rate of about 0.4 per cent per year by the time the classic Industrial Revolution period was completed.
At first sight, this may seem to undermine McCloskey’s claim that ‘ingenuity rather than abstention governed the industrial revolution’ (1981, p. 108) which was made at a time when Deane and Cole’s estimates of economic growth during the Industrial Revolution were the conventional wisdom and, based on these numbers, Feinstein (1981) estimated TFP growth of 1.3 per cent per year during 1801–1830. Replacing Deane and Cole’s growth estimates with my 1985 figures and even more so with the revisions by Broadberry et al. (2015) leads to much lower TFP growth estimates, as we have seen, and an estimate that TFP growth contributes only about 30 per cent of output growth even in 1830–1860. However, if, as is more appropriate, the focus is on the sources of labour
productivity growth, then it is immediately apparent that McCloskey was right and that TFP growth rather than physical-capital deepening accounted for the lion’s share of labour productivity growth (Table 2.5).
Neoclassical growth accounting of this kind is a standard technique and valuable for benchmarking purposes, if nothing else. However, it does potentially underestimate the contribution of new technology to economic growth if technological progress is embodied in new types of capital goods, as was set out in detail by Barro (1999). This was surely the case during the Industrial Revolution; as Feinstein put it, ‘many forms of technological advance … can only take place when
“embodied” in new capital goods. The spinning jennies, steam engines and blast furnaces were the
“embodiment” of the industrial revolution’ (1981, p. 142).
To allow for embodiment effects and to capture the idea of ‘revolutionized’ activities, it is possible to modify a growth accounting equation to distinguish between different types of capital and different sectors, along the following lines
Δln(Y/L) = αOΔln(KO/L) + αNΔln(KN/L) + γΔlnAO + ΦΔlnAN
where the subscripts O and N denote capital in the old and new sectors, respectively, γ and Φ are the gross output shares of these sectors, and αO and αN are the factor shares of the capital used in these sectors.1 Disaggregation can be taken as far as the data permit.
Table 2.6 shows the results of an exercise of this kind. The ‘modernized sectors’ (cottons, woollens, iron, canals, ships and railways) are found to have contributed 0.45 out of 0.71 per cent per year growth in labour productivity over the period 1780–1860 with the majority of this, 0.34 compared with 0.11 per cent, coming from TFP growth as opposed to capital deepening. If the contribution of technological change to the growth of labour productivity is taken to be capital deepening in the modernized sectors plus total TFP growth, then this equates to 0.62 out of 0.71 per cent per year. It remains perfectly reasonable, therefore, to regard technological innovation as responsible for the acceleration in labour productivity growth that marked the importance of the Industrial Revolution as an historical discontinuity as Kuznets would have supposed even though the change was less dramatic than used to be thought.
Table 2.6 Contributions to labour productivity growth, 1780–1860 (% per year)
Capital deepening 0.20
Modernized sectors 0.11
Other sectors 0.09
TFP growth 0.51
Modernized sectors 0.34
Other sectors 0.17
Labour productivity growth 0.71
Memorandum items
Labour force growth 1.22
Capital income share (%) 35
Modernized sectors 5.2
Note: Derived using standard neoclassical growth accounting formula modified to allow for two types of capital. Modernized sectors are textiles, iron and transport.
Source: Crafts (2004a) updated to incorporate new output growth estimates from Broadberry et al. (2015) and revised to a three-factor growth accounting framework.
It may seem surprising that the Industrial Revolution delivered such a modest rate of technological progress given the inventions for which it is famous including most obviously those related to the arrival of steam as a general purpose technology. It should be noted, however, that the well-known stagnation of real wage rates during this period is strong corroborative evidence that TFP growth, which is equal to the weighted average of growth in factor rewards (Barro, 1999), was modest.
Two points can be made straightaway. First, the impact of technological progress was very uneven as is implied by the estimates in Table 2.6. Most of the service sector other than transport was largely unaffected. Textiles, metals and machine-making accounted for less than a third of industrial employment – or 13.4 per cent of total employment – even in 1851 (Shaw-Taylor, 2009) and much industrial employment was still in ‘traditional’ sectors. Second, the process of technological advance was characterized by many incremental improvements and learning to realize the potential of the original inventions. This took time in an era where scientific and technological capabilities were still very weak by later standards.
Steam power offers an excellent example. The estimates in Table 2.7 show that its impact on
productivity growth before 1830 was trivial – as was made clear by the detailed quantitative research of von Tunzelmann (1978) and Kanefsky (1979). In 1830, only about 165,000 horsepower were in use, the steam engine capital share was 0.4 per cent and the Domar weight for steam engines was 1.7 per cent (Crafts, 2004a). The cost effectiveness and diffusion of steam power was held back by the high coal consumption of the original low-pressure engines and the move to high pressure – which benefited not only factories but railways and steam ships – was not generally accomplished until the second half of the nineteenth century. The science of the steam engine was not well understood and the price of steam power fell very slowly compared with that of computers in modern times, especially before about 1850. The maximum impact of steam power on British productivity growth was delayed until the third quarter of the nineteenth century – nearly 100 years after James Watt’s patent.
Table 2.7 Steam’s contribution to British labour productivity growth, 1760–1910 (% per year) 1760–1800 1800–1830 1830–1850 1850–1870 1870–1910
Capital deepening 0.004 0.02 0.16 0.20 0.15
Steam engines 0.004 0.02 0.02 0.06 0.09
Railways 0.14 0.12 0.01
Steamships 0.02 0.05
TFP growth 0.005 0.001 0.04 0.21 0.16
Steam engines 0.005 0.001 0.02 0.06 0.05
Railways 0.02 0.14 0.06
Steamships 0.01 0.05
Total 0.01 0.02 0.20 0.41 0.31
Note: Based on standard neoclassical growth accounting formula disaggregated to include three types of steam capital.
Source: Crafts (2004b).